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<p>A positive integer <i>m</i> is called a <i>Hall number</i> if any finite group of order precisely divisible by <i>m</i> has a Hall subgroup of order <i>m</i>. We prove that, except for the obvious examples, the three integers 12, 24 and 60 are the only Hall numbers, solving a problem proposed by Jiping Zhang.</p>

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The Exceptional Hall Numbers

  • 期刊论文

  • 发表日期：

    2025年5月30日

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  • Zheng Guo,
  • Yong Hu,
  • Cai-Heng Li

摘要

A positive integer m is called a Hall number if any finite group of order precisely divisible by m has a Hall subgroup of order m. We prove that, except for the obvious examples, the three integers 12, 24 and 60 are the only Hall numbers, solving a problem proposed by Jiping Zhang.